Modern LLM GPU fleets are provisioned for worst-case context lengths that the vast majority of requests never approach, wasting GPU capacity on idle KV-cache slots. We present FleetOpt, a framework that starts from first principles: given a workload's prompt-length CDF and a P99 TTFT target, derive the minimum-cost fleet analytically, then deploy it in practice. The analytical core models each pool as an M/G/c queue and derives that the minimum-cost fleet is a two-pool architecture -- a short-context pool and a long-context pool -- with an optimal boundary B* satisfying an equal marginal GPU cost condition across both pools. The fundamental barrier to achieving B* is the cost cliff: a hard routing step where requests just above B* consume 8x--42x more GPU capacity than requests just below it (depending on the context window ratio), creating a structural disincentive to lower the boundary. Compress-and-Route (C&R) is the implementation mechanism that resolves this barrier. Gateway-layer extractive compression trims borderline requests below B* before the engine ever sees them, converting the hard hardware boundary into a software parameter read from the workload CDF. The two components are unified in the FleetOpt offline planner: given a CDF and SLO, it returns the optimal (n_s*, n_l*, B*, gamma*) in under 1 ms. On three production traces, the combined framework reduces total GPU cost by 6--82% versus a homogeneous fleet, with C&R contributing 1--44 percentage points beyond plain pool routing depending on workload archetype. The analytical model is validated against a discrete-event simulator (inference-fleet-sim) with <= 3% error on predicted GPU utilization across all pools and workloads.